Intro to MSA of Continuous Data - Part 9: %Tolerance for One-sided Specs

This is the ninth in a series of articles about MSA. The focus of this article will be on discussing the proper approach to evaluating Repeatability and Reproducibility as a % of Tolerance when the tolerance is one-sided.

The AIAG MSA manual is silent on this and no other "guru" that I am aware of has spoken on it. This is probably because there is no one, right answer.

A recent post asked this question, and I recalled several prior posts that had all asked similar questions, with mixed responses. It forced me to really think the matter through from the perspective of what is the intent of the %Tolerance metric, not what is convenient or easy.
Minitab users have two options. If they enter a natural boundary as the second specification (or the range between the boundary and the specification), Minitab will calculate %Tolerance the same way as if they entered a two sided specification (think Cp). If they leave the other specification blank, Minitab will calculate %Tolerance using 3 * the total R&R and the difference between the study mean and the specification (think Cpk). See the full explanation here.

Lets look a few scenarios, and I will give you my . This is not based on any research or statistics, but simply by thinking the problem through rationally.

Scenario 1, Maximum Flatness: Zero is a natural boundary and there is a maximum allowable flatness specification. Presumably, there is some incentive to drive for smaller and smaller levels of flatness, thus moving farther and farther away from the USL. In this situation, you will conceivably utilize the entire tolerance spectrum. This would tend to justify using the whole range, or entering 0 as a LSL.

Scenario 2, Minimum Hardness: I am using the example used by Minitab in the above link. In this scenario, you are not going to strive for infinite hardness. There will be practical and economical reasons for you to "hover" a safe distance above the LSL, and to not increase over time. In this scenario, it would make more sense to use the Minitab approach. (I will casually overlook the fact that you cannot enter infinity into the USL field).

Scenario 3, Maximum activation force: The same logic could apply to a maximum activation force for a push button. If you strove for zero activation force on a conventional spring-loaded design, there would no force left to reopen the switch. Therefore, you will also “hover” a safe distance below the maximum force and not decrease over time. In this case, the Minitab approach of leaving the LSL field blank would also make sense.

It may make more sense to forget about the %Tolerance entirely and use the Gauge Performance Curve approach (see my file MSA 4th Ed ANOVA.xls in my earlier blog. This approach provides the probability of accepting a product for each specific measurement as you near the specification.

Bottom line, I recommend that you think carefully about your specific situation, and choose the appropriate approach based on the situation.